Chapter 17, Problem 99A

To determine

The coefficient of friction for the waxed floor.

Answer to Problem 99A

The coefficient of friction for the waxed floor is $0.18$ .

Explanation of Solution

Given:

The speed of the child is $v=4.7\text{m}/\text{s}$ .

The slid distance is $d=6.2\text{ m}$ .

Formula used:

The expression for kinetic energy is,

  $KE=\frac{1}{2}m{v}^2$

Here, $m$ is the mass and $v$ is the speed.

The expression for the work done is,

  $W=mgd$

Here, $m$ is the mass, $g$ is the acceleration due to gravity, and $d$ is the distance.

Calculation:

Consider the acceleration due to gravity as $g=9.8\text{m}/{\text{s}}^{\text{2}}$ .

Consider the work done by the waxed floor is equal to the initial kinetic energy of the child.

  $\begin{array}{l}KE=W\\ \frac{1}{2}m{v}^2={\mu }_{\text{k}}mgd\\ {\mu }_{\text{k}}=\frac{v^2}{2gd}\end{array}$

The coefficient of friction is,

  $\begin{array}{l}{\mu }_{\text{k}}=\frac{v^2}{2gd}\\ {\mu }_{\text{k}}=\frac{{\left(4.7\text{m}/\text{s}\right)}^2}{2\times \left(9.8\text{m}/{\text{s}}^{\text{2}}\right)\times \left(6.2\text{ cm}\right)}\\ {\mu }_{\text{k}}=0.18\end{array}$

Conclusion:

Thus, the coefficient of friction for the waxed floor is $0.18$ .